Linear stability analysis [1]} indicates that increasing the surface tension parameter \(\sigma \)  acts to make the interface less unstable, and nonlinear numerical simulations and experiments [2]}, [3]}, [4]} show that increasing \(Q\) , which is mathematically equivalent to decreasing \(\sigma \) , results in an increase in the number of fingers that develop. We perform numerical simulations for a fixed injection rate with values of surface tension varying over several orders of magnitude with the initial condition
\( s(\theta , 0) = 1 + \varepsilon \left( \cos m \theta + \sin n \theta \right),\) 
